The level of daily stock returns is generally regarded as unpredictable. Instead of the level, we focus on the signs of these returns and generate forecasts using various statistical classification techniques, such as logistic regression, generalized additive models, or neural networks. The analysis is carried out using a data set consisting of all stocks that were part of the Dow Jones Industrial Average in 1996. After selecting the relevant explanatory variables in the subsample from 1996 to 2003, forecast evaluations are conducted in an out-of-sample environment for the period from 2004 to 2017. Since the model selection and the forecasting period are strictly separated, the procedure mimics the situation a forecaster would face in real time. It is found that the sign of daily returns is predictable to an extent that is statistically significant. Moreover, trading strategies based on these forecasts generate positive alpha, even after accounting for transaction costs. This underlines the economic significance of the predictability and implies that there are periods during which markets are not fully efficient.